by Daniel Smith
We sometimes think of philosophy as a search for solutions to perennial problems, and the terms “true” and “false” are used to qualify these solutions. But in fact the effort of the greatest philosophers was directed at the nature of the problems themselves, and the attempt to determine what a true problem was as opposed to a false one. In the “Transcendental Dialectic” of the first Critique, for instance, Kant tells us that the concept of the World (or the universe, the totality of what is) is an illusion, because it is generated from a false problem, derived from the category of causality. The problem of causality stems from the fact that an event A causes event B, B causes C, C causes D, and so on, and that this causal network stretches indefinitely in all directions. If we could grasp the totality of these series, we would have the World; but in fact, we cannot grasp this infinite totality. The true object of the Idea of the world is precisely this problem, this causal nexus. When, rather than grasping it as a problem, we instead think of it as an object (the World), and start posing questions about this object (Is it bounded or endless? Is it eternal or did it have a beginning?), we are in the domain of a transcendental illusion, prey to a false problem. This is why Kant said that an Idea—such as the Soul, the World, or God—is an objectively problematic structure; it is, as Kant said, “a problem to which there is no solution.”28
Deleuze has something similar—though not identical—in mind when he says that the conditions of real experience have the objective structure of a problem. What does it mean to speak of a problem that has an objective existence—and is not simply a subjective obstacle to be overcome on the path to knowledge? The calculus once again provides a clue. Soon after its invention, it was the calculus that seemed to lend credence to the classical view of determinism, a clockwork universe without any novelty, in which the future was completely determined by the past. Differential equations had allowed mathematicians to predict, for instance, the next solar eclipse (Halley), the exact dates of the return of a comet (Lalande), or the fact that there was another body perturbing the orbit of the planet Neptune, which led to the discovery of Pluto (Le Verrier). The success in solving such astronomical problems led to extravagant claims like those of Laplace: eventually every future event will be explainable by the use of differential equations. Today, however, this belief in determinism, as supported by the calculus, has been undermined. The reason is simple: setting up differential equations is one thing, but solving them is quite another. Until the advent of computers, the equations that could be solved tended to be linear equations with convergent series, equations that “describe simple, idealized situations where causes are proportional to effects, and forces are proportional to responses.”29 Thus, early on in the history of the calculus, as Ian Stewart has written, “a process of self-selection set in, whereby equations that could not be solved were automatically of less interest than those that could.”30 The equations that could not be solved tended to be non-linear equations, which described fields whose infinite series diverge—and most differential equations have turned out to be non-linear equations. None the less, in the late 1800s, Henri Poincaré worked out a way to study such equations. Even though an exact solution was not attainable, Poincaré discovered that he could recognize the general patterns the solutions would have to take for the equations he was working with—such as centers, foci, saddle points, and nodes or knots. Today, through the use of computers, much more complicated solution patterns have been discovered, such as the well-known Lorenz attractor. Put simply, the solution to the equation will be found in one of the points in the attractor, but one cannot say in advance which point it will be, since the series defined by the equation diverge. This is why we cannot predict the weather more accurately—not because we ourselves lack knowledge of all the variables, but because the weather system itself is objectively problematic; at every moment in its actuality, it is objectively unassignable which trajectory of the attractor it will follow, since its problematic structure is constituted positively by an infinite set of divergent series, which is none the less entirely determined by the attractor itself.
But what, then, is the modal status of a problem separated from its solutions? This question brings us to the concept of the virtual, which has become one of Deleuze's most well-known concepts. The concept, however, has little to do with the popular notion of “virtual reality”; rather, it concerns the modal status of problematic Ideas. One might be tempted to assume that problems are the locus of possibilities waiting to be realized in their solutions. But Deleuze is strongly critical of the concept of possibility in this context, since it is unable to think the new; nor does it allows us to understand the mechanism of differenciation. The reason is that we tend to think of the possible as somehow “pre-existing” the real, like the infinite set of possible worlds that exist in God's understanding before the act of creation (Leibniz). The process of realization, Deleuze suggests, is then subject to two rules: a rule of resemblance and a rule of limitation. On the one hand, the real is supposed to resemble the possible that it realizes, which means that every thing is already given in the identity of the concept, and simply has existence or reality added to it when it is “realized.” Moreover, the means by which the possible is realized in existence remains unclear; existence always occurs “as a brute eruption, a pure act or leap that always occurs behind our backs” (DR 211). On the other hand, since not every possible is realized, the process of realization involves a limitation or exclusion by which some possibilities are thwarted, while others “pass” into the real. With the concept of possibility, in short, everything is already given; everything has already been conceived, if only in the mind of God (the theological presuppositions of the modal logic of possible words are not difficult to discern).31 Instead of grasping existence in its novelty, Deleuze writes, “the whole of existence is here related to a pre-formed element, from which everything is supposed to emerge by a simple ‘realization’” (B 20; cf. 98).
In describing the modal status of problematic multiplicities, Deleuze proposes replacing the concept of the possible with the concept of the virtual, and substituting for the possible–real opposition the virtual–real complementarity. This is much more than a question of words or semantics. The virtual, as Deleuze formulates it, is not subject to a process of realization, but rather a process of actualization, and the rules of actualization are not resemblance and limitation, but rather divergence and difference—in other words, creation and novelty. “Problematic” and “virtuality,” in this sense, are strictly correlative concepts in Deleuze's work. A problem is an objectively determined structure that can be thought apart from its (actual) solutions; it is a virtual multiplicity that is completely differentiated, with its differential relations, its reciprocally determined elements, its singularities, and its convergent and divergent series.32 Yet the “essence” of a virtual multiplicity (or problem) is to actualize itself, to be actualized (or resolved); and in being actualized, it differs from itself, it necessarily becomes differenciated—that is, it produces difference, it is the production of the new.33 The condition does not resemble the conditioned (any more than an egg resembles an adult), and the transcendental is not conceived in the image of the empirical. This is precisely how Deleuze fulfills the requirement that, in the conditions of the real, the different must relate to the different through difference itself (DR 299), which he summarizes in the complex notion of “differen t/c iation” (DR 246): a problem is completely differentiated (with a t)—that is, it is constituted by difference through and through (the differential relation, divergent series)—and in being actualized, it necessarily differenciates itself (with a c)—that is, it creates a new difference. “The entire Idea is caught up in the mathematical-biological system of differen t/c iation” (DR 220).
Thus, at every moment, my existence—like that of a weather system—is objectively problematic, which means that it has the structure of a problem, constituted by virtual elements and divergent series, and the exact trajector
y that “I” will follow is not predictable in advance. In a moment from now, I will have actualized certain of those virtualities: I will have, say, spoken or gestured in a certain manner. In doing so, I will not have “realized a possibility” (in which the real resembles an already-conceptualized possibility), but will have “actualized a virtuality”—that is, I will have produced something new, a difference (the actual does not resemble the virtual in the way that the real resembles the possible). Moreover, when I actualize a virtuality, or resolve a problem, that does not mean that the problematic structure has disappeared. The next moment, so to speak, still has a problematic structure, but one that is now modified by the actualization that has just taken place. In other words, the actualization of the virtual also produces the virtual; the actual and the virtual are like the recto and verso of a single coin. This is what Deleuze means when he says that conditions and the conditioned are determined at one and the same time, and that conditions can never be larger than what they condition—thus fulfilling the Maimonian demands for the conditions of real experience. It is precisely for this reason that we can say, even speaking of ourselves, that every event is new, even though the new is never produced ex nihilo and always seems to fit into a pattern (this pattern is what we call, in psychic systems, our “character”).
Finally, we can introduce a last form of difference into our deduction: intensity, or a difference of potential, which Deleuze analyzes in the fifth chapter of Difference and Repetition (DR 222–61). Why does Deleuze need to add this final concept of difference to his description of the transcendental field, or the conditions of the real? We have been speaking, out of convenience and habit, as if the actualization of the virtual produced a new thing (such as a perception), but of course this cannot be the case, since any differenciation of difference produces a new difference, which is, precisely, a relation and not a thing. Intensity, or difference in potential—to use the language of physics—is Deleuze's term for this new type of relation, which is derived from the comparison of powers expressed in any differential relation (y2/x = P). “A state of affairs or ‘derivative function’ … does not actualize a virtual without taking from it a potential that is distributed in the system of coordinates” (WP 122; cf. DR 174–5). What, then, is this “difference of potential”? Deleuze uses various terms to describe it—intensity, disparity, the unequal-in-itself (and these are not all equivalent)—but perhaps the most telling phrase is that of “the dark precursor,” which is a French term for the ominous signs that herald the onset of a storm. A bolt of lightning is a phenomenon that finds its condition in the buildup of an electrostatic charge in a cloud—that is, in the difference of potential between a negative and positive charge; the flash itself, when it occurs, is a “cancelling out” of this difference. This example provides a clue for understanding Deleuze's broader claim: namely, that intensity, or a difference of potential, is the condition of everything that appears. It is the reason of the sensible, the noumenon closest to the phenomenon (D 31). “Every phenomenon refers to an inequality by which it is conditioned … Every change refers to a difference which is its sufficient reason” (DR 222). And just as differentials must disappear in the solutions of a problem (DR 177–8), intensities necessarily cancel themselves out in the phenomena to which they give rise. Deleuze's analyses of the concept of intensity are among his most complex, but at one point he offers a highly concrete example of the notion, drawn from an everyday experience. At a party, I am hungry, so I go to a table a few feet away and grab an hors d’œuvre; a difference of potential is here opened up between my sensation of hunger and my perception of the food. My movement in space finds its sufficient reason in this difference of potential, and a kind of equalization of this difference in potential occurs when I pick up the hors d’œuvre and ingest the food. Yet this “cancelling out” of the difference does not mean it has disappeared, but that a new difference of potential has opened up: having satiated my hunger, I turn around and see a friend with whom I enter into conversation. It is precisely the new that links up virtual problems with their actualization in an intensity; the new “emerges like the act of solving such a problem, or—what amounts to the same thing—like the actualization of a potential and the establishing of communication between disparates” (DR 246).
With this we break off the deduction, somewhat arbitrarily, since our aim was not to explicate all of Deleuze's concepts, but to follow a rather specific trajectory through Deleuze's thinking about the problem of the new. First, there is the demarcation of the problem of the conditions of real experience, as opposed to what is logically possible or the conditions of possible experience. Second, there is the twofold demarcation of what it means to talk about conditions of real experience (or the new), derived from the work of Salomon Maimon: one must seek the genetic elements of real experience, and one must posit a principle of difference as the fulfillment of this demand. Finally, Deleuze finds in the model of the calculus various concepts of difference (the differential relation, singularities, multiplicities, and so on) that serve to demarcate a transcendental field that is both virtual and problematic, and which serves to define the conditions of real experience. For Deleuze, Being itself always presents itself under a problematic form, which means that it is constituted, in its actuality, by constantly diverging series: that is, by the production of the new. The resuscitation of a positive conception of divergent series, following the advent of non-Euclidian geometries and the new algebras, itself represents a kind of Copernican revolution in contemporary mathematics.34 And Deleuze's philosophy of difference—in part derived from these mathematical advances—represents a Copernican revolution of its own in philosophy, in so far as it makes the problem of the new (difference) not simply a question to be addressed in a remote region of metaphysics, but rather the primary determination of Being itself.
ESSAY 15
The Open
The Idea of the Open: Bergson's Theses on Movement
B
ergson put forward the thesis that “the open is the whole,” and in this essay I would like to explore Bergson's idea of the open, as well as the manner in which Deleuze appropriated and made use of it in his own work.1 The concept of the open, to be sure, is not unique to Bergson. Heidegger proposed his own concept of the open; there are poems by Rilke and Hölderlin on the open, which Heidegger picked up on and discussed; and Giorgio Agamben has recently written a book on the topic.2 While I will not discuss these other writers, it is clear that the theme of the open is an important concern in contemporary philosophy. Despite the enormous differences between Heidegger and Bergson, they seem to have been in agreement in linking together three notions:
1. the whole, or totality
2. the open, or the idea of opening; and
3. time and temporality, or what Bergson calls duration.
It is the interrelation that Bergson establishes between these three notions that I would like to examine in what follows.
BERGSON'S METHOD OF INTUITION
Bergson called his methodological approach “intuition”—perhaps an ill-fated terminological choice, since what Bergson means by this term has little to do with its use in everyday language (as in the phrase “woman's intuition”) or in mathematics. For Bergson, the world is a world of mixtures—what is given to us in experience are always mixtures or complexes of space-time (10 Nov 1981)—and Bergson utilizes the term “intuition” to describe the method through which one can comprehend the mixtures that are given to us in experience. The method has three aspects:
1. The task of philosophy is to analyze these mixtures.
2. To analyze is to seek out what is pure in any given mixture.
3. What is pure in a mixture are not elements but tendencies.3
For instance, the act of recognizing a friend in a hallway is a mixture that implies both perception (I see the person in front of me) and memory (I recognize them because I have a memory of their face). In Matter and Memory, Bergson therefore attempted to
create concepts of pure perception and pure memory; since perception and memory are mixed in experience, we will have a confused conception of even a simple act of recognition if we are unable to separate out the isolatable “tendencies” of perception and memory. Deleuze and Guattari, in Capitalism and Schizophrenia, adopted this Bergsonian method when they isolated the concept of four “pure” social formations—primitive territorialities, States, capitalism, the war machine—even though in fact these types are only ever encountered in experience in concrete mixtures. It is only when we have isolated these pure concepts that we can begin to analyze the complexities of the mixtures found in any given social assemblage. In a similar manner, Deleuze will arrive at the Idea of the Open through an application of Bergson's method of intuition to the problem of movement. The question Bergson asks is: What is pure movement? What is movement as a pure tendency? At the beginning of The Movement-Image (MI 1–11), Deleuze summarizes Bergson's analyses of movement in terms of three theses, which I would like to use to structure the comments that follow:
1. Movement is distinct from the space covered.
2. The instant is an immobile section of movement.
3. Movement is a mobile section of duration (movement expresses a change in duration or the Whole, which is equivalent to the Open).
BERGSON'S FIRST THESIS: MOVEMENT IS DISTINCT FROM SPACE COVERED
Bergson's first thesis is that we have a tendency to confuse movement with the space traversed. Zeno's famous paradox of movement, for instance, depends on this confusion: Achilles will never catch up with the tortoise, or an arrow will never reach its target, because in order to reach its target, it first has to traverse half the space to the target, and then half of the remaining space, and then half of that remaining space, and so on to infinity. But Zeno, Bergson argues, confuses the movement of the arrow with the space traversed by the arrow. The space traversed is discrete or divisible, and divisible to infinity, whereas movement, as the act of traversing that space, is indivisible or continuous. In his first thesis, Bergson establishes a categorical opposition between divisible space and indivisible movement: movement is not a divisible space, but an indivisible duration. Bergson then gives us a second presentation of his first thesis. If we begin with divisible space, as Zeno does, we can indeed reconstitute movement, but we can reconstitute it only as a succession: that is, as a succession of positions in space or a succession of moments in time. In Creative Evolution, Bergson will call this the cinematographic illusion, the illusion through which cinema works; twenty-four immobile frames per second pass through the projector, but these immobile frames produce the illusion of movement taking place in a uniform time. Indeed, it is from these two notions—immobile frames or sections, and the form of succession to which we subject them—that we derive the idea of an abstract, homogeneous, equalizable, and uniform time. But this uniform conception of time misses the nature of movement for two obvious reasons. First, it tries to reconstitute movement out of something that is not movement: that is, out of immobile frames or instants. (Philosophers are doing nothing other when they utilize the symbolism of T1, T2, T3, and so on, to analyze time.) Second, and more importantly, no matter how close the immobile instants are, there is always an interval between the two instances—and movement will always be happening in the interval, and not at the instant (no matter how small the interval may be). This is another way of saying that movement always takes place behind the back of the thinker. One can multiply the immobile cuts—the positions in space or the moments in time—but it is not by multiplying the immobile cuts that one can reconstitute movement.